The optimization problem (REF ) is well-known in the statistical literature as a Procrustes problem [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
Our recasting of the DMD regression as a Procrustes problem
is a new connection, and is the basis of piDMD.
This perspective enables us to leverage the substantial extant work on Procrustes problems into new application areas.
The literature contains many exact solutions for Procrustes problems,
including notable cases of orthogonal matrices [9]},
and symmetric matrices [5]}.
